Carl P. Goodrich, Andrea J. Liu, Sidney R. Nagel
We present an analysis of finite-size effects in jammed packings of N soft, frictionless spheres at zero temperature. Sufficiently close to the jamming transition, there is a 1/N correction to the discrete jump in the contact number at the transition so that jammed packings exist only above isostaticity. As a result, the contact number and elastic moduli exhibit power law scaling only at higher pressures. The crossover in these quantities with pressure obeys scaling collapse as a function of N in both 2 and 3 dimensions, indicating that the jamming transition has an upper critical dimension of 2.
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http://arxiv.org/abs/1204.4915
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